Publications

For all papers listed on this page, the given links are to a preprint version, not to the cited published version.

2026#

Gianluca Ceruti, Jonas Kusch, Christian Lubich, Dominik Sulz, A parallel basis update and Galerkin integrator for tree tensor networks, SIAM J. Sci. Comput. 48 (2026), A27-A48.

2025#

Dominik Edelmann, Balázs Kovács, Christian Lubich, Numerical analysis of an evolving bulk-surface model of tumour growth, IMA J. Numer. Anal. 45 (2025), 2581-2627.
Gianluca Ceruti, Daniel Kressner, Dominik Sulz, Low-Rank Tree Tensor Network Operators for Long-Range Pairwise Interactions, SIAM J. Sci. Comput. 47 (2025), A2248-A2271.
Jörg Nick, Selina Burkhard, Christian Lubich, Time-dependent electromagnetic scattering from dispersive materials, IMA J. Numer. Anal. 45 (2025), 2545-2580.
Nicola Guglielmi, Christian Lubich, Transient dynamics under structured perturbations: bridging unstructured and structured pseudospectra, SIAM J. Numer. Anal. 63 (2025), 908-930.

2024#

Gianluca Ceruti, Lukas Einkemmer, Jonas Kusch, Christian Lubich, A robust second-order low-rank BUG integrator based on the midpoint rule, BIT Numer. Math. 64, 30 (2024).
Yanyan Shi, Drift approximation by the modified Boris algorithm of charged-particle dynamics in toroidal geometry, Numer. Math. 156 (2024), 1197-1217.
Gianluca Ceruti, Jonas Kusch, Christian Lubich, A parallel rank-adaptive integrator for dynamical low-rank approximation, SIAM J. Sci. Comput. 46 (2024), B205-B228.
Jörg Nick, Numerical analysis for electromagnetic scattering from nonlinear boundary conditions, Math. Comp. 93 (2024), 1529-1568.
Dominik Sulz, Christian Lubich, Gianluca Ceruti, Igor Lesanovsky, Federico Carollo, Numerical simulation of long-range open quantum many-body dynamics with tree tensor networks, Phys. Rev. A 109 (2024), 022420.
Julian Baumstark, Tobias Jahnke, Christian Lubich, Polarized high-frequency wave propagation beyond the nonlinear Schrödinger approximation, SIAM J. Math. Anal. 56 (2024), 454-473.

2023#

Ernst Hairer, Christian Lubich, Yanyan Shi, Leapfrog methods for relativistic charged-particle dynamics, SIAM J. Numer. Anal. 61 (2023), 2844-2858.
Nicola Guglielmi, Christian Lubich, Stefano Sicilia, Rank-1 matrix differential equations for structured eigenvalue optimization, SIAM J. Numer. Anal. 61 (2023), 1737-1762.
Gianluca Ceruti, Christian Lubich, Dominik Sulz, Rank-adaptive time integration of tree tensor networks, SIAM J. Numer. Anal. 61 (2023), 194-222.
Christian Lubich, Yanyan Shi, On a large-stepsize integrator for charged-particle dynamics, BIT Numer. Math. 63, 14 (2023).

2022#

Gianluca Ceruti, Jonas Kusch, Christian Lubich, A rank-adaptive robust integrator for dynamical low-rank approximation, BIT Numer. Math. 62 (2022), 1149-1174.
Ernst Hairer, Christian Lubich, Yanyan Shi, Large-stepsize integrators for charged-particle dynamics over multiple time scales, Numer. Math. 151 (2022), 659-691.
Jörg Nick, Balázs Kovács, Christian Lubich, Time-dependent electromagnetic scattering from thin layers, Numer. Math. 150 (2022), 1123-1164.
Gianluca Ceruti, Christian Lubich, An unconventional robust integrator for dynamical low-rank approximation, BIT Numer. Math. 62 (2022), 23-44.
Lehel Banjai, Christian Lubich, J&oumlrg Nick, Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature, IMA J. Numer. Anal. 42 (2022), 1-26.
Jonas Kusch, Gianluca Ceruti, Lukas Einkemmer, Martin Frank, Dynamical low-rank approximation for Burgers’ equation with uncertainty, International Journal for Uncertainty Quantification 12 (5).

2021#

Balázs Kovács, Buyang Li, Christian Lubich, A convergent evolving finite element algorithm for Willmore flow of closed surfaces, Numer. Math. 149 (2021), 595-644.
Antonio Fazzi, Nicola Guglielmi, Christian Lubich, Finding the nearest passive or nonpassive system via Hamiltonian eigenvalue optimization, SIAM J. Matrix Anal. Appl. 42 (2021), 1553-1580.
Georgios Akrivis, Michael Feischl, Balázs Kovács, Christian Lubich, Higher-order linearly implicit full discretization of the Landau-Lifschitz-Gilbert equation, Math. Comp. 90 (2021), 995-1038.
Dominik Edelmann, Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains, SMAI J. Comput. Math. 7 (2021), 57-73.
Jörg Nick, Balázs Kovács, Christian Lubich, Correction to: Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations, Numer. Math. 147 (2021), 997-1000.
Gianluca Ceruti, Christian Lubich, Hanna Walach, Time integration of tree tensor networks, SIAM J. Numer. Anal. 59 (2021), 289-313.
Eleonora Andreotti, Dominik Edelmann, Nicola Guglielmi, Christian Lubich, Measuring the stability of spectral clustering, Linear Algebra Appl. 610 (2021), 673-697.

2020#

Caroline Lasser, Christian Lubich, Computing quantum dynamics in the semiclassical regime, Acta Numerica 29 (2020), 229-401.
Balázs Kovács, Buyang Li, Christian Lubich, A convergent algorithm for forced mean curvature flow driven by diffusion on the surface, Interfaces and Free Boundaries 22 (2020), 443-464.
Gianluca Ceruti, Christian Lubich, Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors, BIT 60 (2020), 591-614.
Ernst Hairer, Christian Lubich, Bin Wang, A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field, Numer. Math. 144 (2020), 787-809.
Ernst Hairer, Christian Lubich, Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field, Numer. Math. 144 (2020), 699-728.

2019#

Balázs Kovács, Buyang Li, Christian Lubich, A convergent evolving finite element algorithm for mean curvature flow of closed surfaces, Numer. Math. 143 (2019), 797-853.
Lukas Einkemmer, Christian Lubich, A quasi-conservative dynamical low-rank algorithm for the Vlasov equation, SIAM J. Sci. Comput. 41 (2019), B1061–B1081.
Alexander Ostermann, Chiara Piazzola, Hanna Walach, Convergence of a low-rank Lie-Trotter splitting for stiff matrix differential equations, SIAM J. Numer. Anal., 57(4), 1947–1966.
Lehel Banjai, Christian Lubich, Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations, IMA J. Numer. Anal. 39 (2019), 1134-1157.
Eleonora Andreotti, Dominik Edelmann, Nicola Guglielmi, Christian Lubich, Constrained graph partitioning via matrix differential equations, SIAM J. Matrix Anal. Appl. 40 (2019), 1-22.

2018#

Ernst Hairer, Christian Lubich, Energy behaviour of the Boris method for charged-particle dynamics, BIT 58 (2018), 969-979.
Lukas Einkemmer, Christian Lubich, A low-rank projector-splitting integrator for the Vlasov-Poisson equation, SIAM J. Sci. Comput. 40 (2018), B1330-B1360.
Peer Kunstmann, Buyang Li, Christian Lubich, Runge–Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity, Found. Comput. Math. 18 (2018), 1109-1130.
Balázs Kovács, Christian Lubich, Linearly implicit full discretization of surface evolution, Numer. Math. 140(1) (2018), 121-152.
Christian Lubich, Bart Vandereycken, Hanna Walach, Time integration of rank-constrained Tucker tensors, SIAM J. Numer. Anal. 56 (2018), 1273-1290.
Balázs Kovács, Christian Power, Maximum norm stability and error estimates for the evolving surface finite element method, NMPDE 34(2) (2018), 518-554.
Balázs Kovács, Christian Power, Higher-oder time discretizations with ALE finite elements for parabolic problems on evolving surfaces, IMA J. Numer. Anal. 38(1) (2018), 460-494. doi:10.1093/imanum/drw074.
Balázs Kovács, High-order evolving surface finite element method for parabolic problems on evolving surfaces, IMA J. Numer. Anal. 38(1) (2018), 430-459. doi:10.1093/imanum/drx013
Balázs Kovács, Christian Lubich, Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type, Numer. Math. 138 (2018), 365-388.

2017#

Nicola Guglielmi, Christian Lubich, Matrix stabilization using differential equations, SIAM J. Numer. Anal. 55 (2017), 3097-3119.
Balázs Kovács, Buyang Li, Christian Lubich, Christian Power-Guerra, Convergence of finite elements on an evolving surface driven by diffusion on the surface, Numer. Math. 137 (2017), 643-689.
Ernst Hairer, Christian Lubich, Symmetric multistep methods for charged-particle dynamics, SMAI J. Comput. Math. 3 (2017), 205-218.
Nicola Guglielmi, Christian Lubich, Volker Mehrmann, On the nearest singular matrix pencil, SIAM J. Matrix Anal. Appl. 38 (2017), 776-806.
Balázs Kovács, Christian Lubich, Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations, May 2016, revised January 2017. To appear in Numer. Math. 137 (2017), 91-117.
Benedikt Kloss, Irene Burghardt, Christian Lubich, Implementation of a novel projector-splitting integrator for the multi-configurational time-dependent Hartree approach, J. Chem. Phys. 146 (2017), 174107.
Georgios Akrivis, Buyang Li, Christian Lubich, Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations, Math. Comp. 86 (2017), 1527-1552.
Balázs Kovács, Christian Lubich, Numerical analysis of parabolic problems with dynamic boundary conditions, IMA J. Numer. Anal. 37 (2017), 1-39.

2016#

Balázs Kovács, Buyang Li, Christian Lubich, A-stable time discretizations preserve maximal parabolic regularity, SIAM J. Numer. Anal. 54 (2016), 3600-3624.
Ludwig Gauckler, Ernst Hairer, Christian Lubich, Long-term analysis of semilinear wave equations with slowly varying wave speed, Comm. Partial Differential Equations 41 (2016), 1934-1959.
Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, Frank Verstraete, Unifying time evolution and optimization with matrix product states, Phys. Rev. B 94 (2016), 165116.
Bernd Brumm, Emil Kieri, A matrix-free Legendre spectral method for initial boundary value problems, ETNA 45 (2016), 283-304.
Ernst Hairer, Christian Lubich, Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency, Numer. Math. 134 (2016), 119-138.
Christian Hainzl, Jonathan Seyrich, Comparing the full time-dependent Bogoliubov–de-Gennes equations to their linear approximation: A numerical investigation, Eur. Phys. J. B 89, 1-10 (2016).
Balázs Kovács, Christian Power, Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces, NMPDE 32 (2016), 1200-1231.
Emil Kieri, Christian Lubich, Hanna Walach, Discretized dynamical low-rank approximation in the presence of small singular values, SIAM J. Numer. Anal. 54 (2016), 1020-1038.
Daniela Kunst, Tomáš Ledvinka, Georgios Lukes-Gerakopoulos, Jonathan Seyrich, Comparing Hamiltonians of a spinning test particle for different tetrad fields, Phys. Rev. D 93, 044004 (2016).

2015#

Georgios Akrivis, Christian Lubich, Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations, Numer. Math. 131 (2015), 713–735.
Christian Lubich, Time integration in the multiconfiguration time-dependent Hartree method of molecular quantum dynamics, Appl. Math. Res. Express 2015, 311-328.
David Cohen, Ludwig Gauckler, Ernst Hairer, Christian Lubich, Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions, BIT 55 (2015), 705-732.
Bernd Brumm, A fast matrix-free algorithm for spectral approximations to the Schrödinger equation, SIAM J. Sci. Comput. 37 (2015), A2003-A2025.
Christian Lubich, Ivan Oseledets, Bart Vandereycken, Time integration of tensor trains, SIAM J. Numer. Anal. 53 (2015), 917-941.
Lehel Banjai, Christian Lubich, Francisco-Javier Sayas, Stable numerical coupling of exterior and interior problems for the wave equation, Numer. Math. 129 (2015), 611-646.
Nicola Guglielmi, Daniel Kressner, Christian Lubich, Low-rank differential equations for Hamiltonian matrix nearness problems, Numer. Math. 129 (2015), 279-319.
Dhia Mansour, Gauss-Runge-Kutta time discretization of wave equations on evolving surfaces, Numer. Math. 129 (2015), 21-54.
Christian Lubich, Dhia Mansour, Variational discretization of wave equations on evolving surfaces, Math. Comp. 84 (2015), 513-542.

2014#

Christian Lubich, Daniel Weiss, Numerical integrators for motion under a strong constraining force, Multiscale Model. Simul. 12 (2014), 1592-1606.
Nicola Guglielmi, Daniel Kressner, Christian Lubich, Computing extremal points of symplectic pseudospectra and solving symplectic matrix nearness problems, SIAM J. Matrix Anal. & Appl. 35 (2014), 1407-1428.
Christian Lubich, Low-rank dynamics, in Extraction of Quantifiable Information from Complex Systems (S. Dahlke et al., eds.), Springer Lecture Notes in Computational Science and Engineering, Vol. 102, Springer, 2014, pp. 381-396.
Georgios Lukes-Gerakopoulos, Jonathan Seyrich, Daniela Kunst, Investigating spinning test particles: Spin supplementary conditions and the Hamiltonian formalism, Phys. Rev. D 90, 104019 (2014).
Erwan Faou, Ludwig Gauckler, Christian Lubich, Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation, Forum Math. Sigma 2, Article ID e5, 45 p. (2014).
Ernst Hairer, Christian Lubich, Energy-diminishing integration of gradient systems, IMA J. Numer. Anal. 34 (2014), 452-461.
Christian Lubich, Ivan Oseledets, A projector-splitting integrator for dynamical low-rank approximation, BIT 54 (2014), 171-188.
Bernd Brumm, Daniel Weiss, Heterogeneous Multiscale Methods for Highly-Oscillatory Mechanical Systems with Solution-Dependent Frequencies, IMA J. Numer. Anal. 34 (2014), 55-82.

2013#

Christian Lubich, Dhia Mansour, Chandrasekhar Venkataraman, Backward difference time discretization of parabolic differential equations on evolving surfaces, IMA J. Numer. Anal. 33 (2013), 1365-1385.
Erwan Faou, Ludwig Gauckler, Christian Lubich, Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus, Comm. Partial Differential Equations 38 (2013), 1123-1140.
Ernst Hairer, Christian Lubich, Long-term control of oscillations in differential equations, Internat. Math. Nachrichten 223 (2013), 1-16.
Ludwig Gauckler, Ernst Hairer, Christian Lubich, Energy separation in oscillatory Hamiltonian systems without any non-resonance condition, Comm. Math. Phys. 321 (2013), 803-815.
Christian Lubich, Charalambos Makridakis, Interior a posteriori error estimates for time discrete approximations of parabolic problems, Numer. Math. 124 (2013), 541-557.
Paola Console, Ernst Hairer, Christian Lubich, Symmetric multistep methods for constrained Hamiltonian systems, Numer. Math. 124 (2013), 517-539.
Christian Lubich, Thorsten Rohwedder, Reinhold Schneider, Bart Vandereycken, Dynamical approximation by hierarchical Tucker and tensor-train tensors, SIAM J. Matrix Anal. Appl. 34 (2013), 470-494.
Nicola Guglielmi, Christian Lubich, Low-rank dynamics for computing extremal points of real pseudospectra, SIAM J. Matrix Anal. Appl. 34 (2013), 40-66.
Jonathan Seyrich, Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion, Phys. Rev. D 87, 084064 (2013).
Helge Holden, Christian Lubich, Nils Henrik Risebro, Operator splitting for partial differential equations with Burgers nonlinearity, Math. Comp. 82 (2013), 173-185.

2012#

Jonathan Seyrich, Georgios Lukes-Gerakopoulos, Symmetric integrator for nonintegrable Hamiltonian relativistic systems, Phys. Rev. D 83, 124013 (2012).
Daniel Weiss, Tassilo Küpper, H.A. Hosham Invariant manifolds for nonsmooth systems, Physica D: Nonlinear Phenomena 241 (2012) 1895-1902.
Ernst Hairer, Christian Lubich, Modulated Fourier expansions for continuous and discrete oscillatory systems, in Foundations of Computational Mathematics: Budapest 2011 (F. Cucker et al., eds.), Cambridge Univ. Press, 2012, 113-128.
Ludwig Gauckler, Ernst Hairer, Christian Lubich, Daniel Weiss, Metastable energy strata in weakly nonlinear wave equations, Comm. Partial Differential Equations 37 (2012), 1391-1413.
Ernst Hairer, Christian Lubich, On the energy distribution in Fermi-Pasta-Ulam lattices, Arch. Ration. Mech. Anal. 205 (2012), 993-1029.
Gerhard Dziuk, Christian Lubich, Dhia Mansour, Runge-Kutta time discretization of parabolic differential equations on evolving surfaces, IMA J. Numer. Anal. 32 (2012), 394-416.

2011#

Lehel Banjai, Christian Lubich, Jens Markus Melenk, Runge-Kutta convolution quadrature for operators arising in wave propagation, Numer. Math. 119 (2011), 1-20.
Lehel Banjai, Christian Lubich, An error analysis of Runge-Kutta convolution quadrature, BIT 51 (2011), 483-496.
Nicola Guglielmi, Christian Lubich, Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking, SIAM J. Numer. Anal. 49 (2011), 1194-1209. Erratum/Addendum, SIAM J. Numer. Anal. 50 (2012), 977-981.
Othmar Koch, Christian Lubich, Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics, IMA J. Numer. Anal. 31 (2011), 379-395.
Ludwig Gauckler, Convergence of a split-step Hermite method for the Gross-Pitaevskii equation, IMA J. Numer. Anal. 31 (2011), 396-415.
Jonas Haehnle, Andreas Prohl, Mumford-Shah-Euler Flow With Sphere Constraint And Applications to Colour Image Inpainting, SIAM J. Imaging Sci. 4 (2011), 1200-1233.
Jonas Haehnle, Numerical Approximations of the Mumford-Shah Functional for Unit Vector Fields, IFBJ Volume 13, Issue 3 (2011), 297-326.

2010#

Christian Lubich, Benny Walther, Bernd Bruegmann, Symplectic integration of post-Newtonian equations of motion with spin, Phys. Rev. D 81 (2010), 104025.
Dajana Conte, Christian Lubich, An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics, M2AN 44 (2010), 759-780.
Othmar Koch, Christian Lubich, Dynamical tensor approximation, SIAM J. Matrix Anal. 31 (2010), 2360-2375.
Erich Carelli, Jonas Haehnle, and Andreas Prohl, Convergence analysis for incompressible generalized Newtonian fluid flows with nonstandard anisotropic growth conditions, SIAM J. Numer. Anal. 48 (2010), 164-190.
Jonas Haehnle, Andreas Prohl, Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions, Math. Comp. 79 (2010), 189-208.
Ludwig Gauckler, Christian Lubich, Splitting integrators for nonlinear Schrödinger equations over long times, Found. Comput. Math. 10 (2010), 275-302.
Ludwig Gauckler, Christian Lubich, Nonlinear Schrödinger equations and their spectral semi-discretizations over long times, Found. Comput. Math. 10 (2010), 141-169.

2009#

Erwan Faou, Vasile Gradinaru, Christian Lubich, Computing semiclassical quantum dynamics with Hagedorn wavepackets, SIAM J. Sci. Comp. 31 (2009), 3027-3041.
Sören Bartels, Christian Lubich, and Andreas Prohl, Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers, Math. Comp. 78 (2009), 1269-1292.
Ernst Hairer, Christian Lubich, Oscillations over long times in numerical Hamiltonian systems, in Highly oscillatory problems (B. Engquist, A. Fokas, E. Hairer, A. Iserles, eds.), London Mathematical Society Lecture Note Series 366, Cambridge Univ. Press, 2009.

2008#

Erwan Faou, Vasile Gradinaru, Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation, IMA Journal of Numerical Analysis 2008; doi: 10.1093/imanum/drn041.
Ronny Richter, Christian Lubich, Free and constrained symplectic integrators for numerical general relativity, Class. Quantum Grav. 25 (2008), 225018.
Achim Nonnenmacher, Christian Lubich, Dynamical low-rank approximation: applications and numerical experiments, Math. Comput. Simulation 79 (2008), 1346-1357.
Christian Lubich, On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations, Math. Comp. 77 (2008), 2141-2153.
David Cohen, Ernst Hairer, Christian Lubich, Conservation of energy, momentum and actions in numerical discretizations of nonlinear wave equations, Numer. Math. 110 (2008), 113-143.
Ernst Hairer, Christian Lubich, Spectral semi-discretisations of weakly nonlinear wave equations over long times, Found. Comput. Math. 8 (2008), 319-334.
David Cohen, Ernst Hairer, Christian Lubich, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, Arch. Ration. Mech. Anal. 187 (2008), 341-368.
Maria Lopez-Fernandez, Christian Lubich, Achim Schädle, Adaptive, fast, and oblivious convolution in evolution equations with memory, SIAM J. Sci. Comp. 30 (2008), 1015-1037.

2007#

Vasile Gradinaru, Strang Splitting for the Time Dependent Schrödinger Equation on Sparse Grids, SIAM J. Num. Analysis 46 (2007), 103-123.
Vasile Gradinaru, Fourier Transform on Sparse Grids: Code Design and Application to the Time Dependent Schrödinger Equation, Computing 80 (2007), 1-22.
Othmar Koch, Christian Lubich, Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics, M2AN 41 (2007), 315-332.
Othmar Koch, Christian Lubich, Dynamical low-rank approximation, SIAM J. Matrix Anal. Appl. 29 (2007), 434-454.

2006#

David Cohen, Tobias Jahnke, Katina Lorenz, Christian Lubich, Numerical integrators for highly oscillatory Hamiltonian systems: a review, in Analysis, Modeling and Simulation of Multiscale Problems (A. Mielke, ed.), Springer, Berlin, 2006, 553-576.
Erwan Faou and Christian Lubich, A Poisson integrator for Gaussian wavepacket dynamics, Comput. Vis. Sci. 9 (2006), 45-55.
David Cohen, Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems, IMA J. Numer. Anal. 26 (2006), 34-59.
Achim Schädle, Maria Lopez-Fernandez, Christian Lubich, Fast and oblivious convolution quadrature, SIAM J. Sci. Comp. 28 (2006), 421-438.
Eduardo Cuesta, Christian Lubich, Cesar Palencia, Convolution quadrature time discretization of fractional diffusion-wave equations, Math.Comp. 75 (2006), 673-696.

2005#

Maria Lopez-Fernandez, Christian Lubich, Cesar Palencia, Achim Schädle, Fast Runge-Kutta approximation of inhomogeneous parabolic equations, Numer. Math. 102 (2005), 277-291.
David Cohen, Ernst Hairer, Christian Lubich, Numerical energy conservation for multi-frequency oscillatory differential equations, BIT 45 (2005), 287-305.
Nicola Guglielmi, Christian Lubich, Numerical periodic orbits of neutral delay differential equations, Discrete Contin. Dyn. Syst. 13 (2005), 1057-1067.
Katina Lorenz, Tobias Jahnke, Christian Lubich, Adiabatic integrators for highly oscillatory second order linear differential equations with time-varying eigendecomposition, BIT 45 (2005), 91-115.
Christian Lubich, On variational approximations in quantum molecular dynamics, Math. Comp.74 (2005), 765-779.

2004#

Christian Lubich, Convolution quadrature revisited, BIT 44 (2004), 503-514.
Ernst Hairer and Christian Lubich, Symmetric multistep methods over long times, Numer. Math. 97 (2004), 699-723.
Christian Lubich, A variational splitting integrator for quantum molecular dynamics, Appl. Numer. Math. 48 (2004), 355-368.

2003#

David Cohen, Ernst Hairer and Christian Lubich, Modulated Fourier expansions of highly oscillatory differential equations, Foundations of Comput. Math. 3 (2003), 327-345.
Ernst Hairer, Christian Lubich, Gerhard Wanner, Geometric numerical integration illustrated by the Störmer-Verlet method, Acta Numerica 2003, 399-450.
Marlis Hochbruck and Christian Lubich, On Magnus integrators for time-dependent Schrödinger equations, SIAM J. Numer. Anal. 41 (2003), 945-963.
Tobias Jahnke and Christian Lubich, Numerical integrators for quantum dynamics close to the adiabatic limit, Numer. Math. 94 (2003), 289-314.

2002#

Harry Yserentant, The convergence of the finite mass method for flows in given force and velocity fields, in: Meshfree Methods for Partial Differential Equations (M. Griebel and M.A. Schweitzer, eds.), Lecture Notes in Computational Science and Engineering 26 (2002).
Klaus Neymeyr, A geometric theory for preconditioned inverse iteration applied to a subspace, Math. Comp. 71 (2002), 197-216.
Christian Lubich, Integrators for quantum dynamics: a numerical analyst’s brief review, in Quantum Simulations of Many-Body Systems: From Theory to Algorithms (J. Grotendorst, D. Marx, A. Muramatsu, eds.), NIC Series Vol. 10, Jülich 2002, 459-466.
Christian Lubich and Achim Schädle, Fast convolution for non-reflecting boundary conditions, SIAM J. Sci. Comput. 24 (2002), 161-182.
Achim Schädle, Non-reflecting boundary conditions for the two-dimensional Schrödinger equation, Wave Motion 35 (2002), 181-188.

2001#

Christian Lubich, On dynamics and bifurcations of nonlinear evolution equations under numerical discretization, in B. Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer, Berlin, 2001, 469-500.
Harry Yserentant, The propagation of sound in particle models of compressible fluids, Numer. Math. (2001) 88: 581-601
Klaus Neymeyr, A geometric theory for preconditioned inverse iteration, I:Extrema of the Rayleigh quotient, Linear Algebra Appl. 332 (2001), 61-85
Klaus Neymeyr, A geometric theory for preconditioned inverse iteration, II:Convergence estimates, Linear Algebra Appl. 332 (2001), 87-104

2000#

Christoph Gauger, Peter Leinen, Harry Yserentant, The Finite Mass Method, November 1999. SIAM J. Numer. Anal. 37 (2000), 1768-1799 PostScript
Tobias Jahnke, Christian Lubich, Error bounds for exponential operator splittings, BIT 40 (2000), 735-744.
Ernst Hairer, Christian Lubich, Energy conservation by Störmer-type numerical integrators, in Numerical Analysis 1999 (D.F. Griffiths, G.A. Watson, eds.), Chapman & Hall/CRC, London (2000), 169-190.
Ernst Hairer, Christian Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations, SIAM J. Numer. Anal. 38 (2000), 414-441.
Ernst Hairer, Christian Lubich, Asymptotic expansions and backward analysis for numerical integrators, in Dynamics of Algorithms (R. de la Llave, L.R. Petzold, J. Lorenz, eds.), Springer IMA Vol. 118, 2000, 91-106.

1999#

Harry Yserentant, Coarse grid spaces for domains with a complicated boundary, Numerical Algorithms 21 (1999), 387-392.
Marlis Hochbruck, Christian Lubich, Exponential integrators for quantum-classical molecular dynamics, BIT 39 (1999), 620-645.
Marlis Hochbruck, Christian Lubich, A Gautschi-type method for oscillatory second-order differential equations, Numer. Math. 83 (1999), 403-426.
Jos L.M. van Dorsselaer, Christian Lubich, Inertial manifolds of parabolic differential equations under higher-order discretizations, IMA J. Numer. Anal. 19 (1999), 455-471.
Harry Yserentant, Particles of variable size, Numer. Math., 82 (1999), pp. 143-159.
Harry Yserentant, Entropy generation and shock resolution in the particle model of compressible fluids, Numer. Math., 82 (1999), pp. 161-177.
Ernst Hairer, Christian Lubich, Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization, Appl. Numer. Math. 29 (1999), 57-71.
Marlis Hochbruck, Christian Lubich, A bunch of time integrators for quantum/classical molecular dynamics, in “Computational Molecular Dynamics: Challenges, Methods, Ideas” (P. Deuflhard et al., eds.), Springer Lecture Notes in Computational Science and Engineering, Vol. 4 (1999), 421-432.

1998#

Christian Lubich, Alexander Ostermann, Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization, Numer. Math. 81 (1998), 53-84.
Marlis Hochbruck, Christian Lubich, and Hubert Selhofer, Exponential integrators for large systems of differential equations, SIAM J. Sci. Comp. 19 (1998), 1552-1574.
Karel in ’t Hout, Christian Lubich, Periodic orbits of delay differential equations under discretization, BIT 38 (1998), 72-91.
Marlis Hochbruck, Christian Lubich, Error analysis of Krylov methods in a nutshell, SIAM J. Sci. Comput. 19 (1998), 695-701.

1997#

Marlis Hochbruck, Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations. J. Comp. Appl. Math. 86 (1997), 219-236.
Marlis Hochbruck, Christian Lubich, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal. 34 (1997), 1911-1925.
Christian Engstler, Christian Lubich, MUR8: a multirate extension of the eighth-order Dormand-Prince method, Appl. Numer. Math. 25 (1997), 185-192, special issue Time Integrators.
Ernst Hairer, Christian Lubich, The life-span of backward error analysis for numerical integrators, Numer. Math. 76 (1997), 441-462.
Harry Yserentant, A particle model of compressible fluids,Numer. Math. 76 (1997), 111-142.
Harry Yserentant, A new class of particle methods,Numer. Math. 76 (1997), 87-109.
Christian Engstler, Christian Lubich, Multirate extrapolation methods for differential equations with different time scales, Computing 58 (1997), 173-185.

1996#

Christian Lubich, Alexander Ostermann, Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour, Appl. Numer. Math. 22 (1996), 279-292, special issue Runge-Kutta Centennial.
Ch. Lubich, I.H. Sloan, V. Thome’e, Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term, Math. Comp. 65 (1996), 1-17.
Martin H. Gutknecht, Marlis Hochbruck, Optimized look-ahead recurrences for adjacent rows in the Padé table, BIT 36:2, pages 264-286, 1996.

1995#

Martin H. Gutknecht, Marlis Hochbruck, The stability of inversion formulas for Toeplitz matrices, Linear Algebra and its Applications 223/224, pages 307-324, 1995.
Peter Leinen, Data Structures and Concepts for Adaptive Finite Element methods, Computing 55, 1995, pages 325-354.
Christian Lubich, Alexander Ostermann, Runge-Kutta approximation of quasi-linear parabolic equations, Math. Comp. 64 (1995), 601-627.
Christian Lubich, Alexander Ostermann, Linearly implicit time discretization of non-linear parabolic equations, IMA J. Numer. Anal. 15 (1995), 555-583.
Christian Lubich, Alexander Ostermann, Interior estimates for time discretizations of parabolic equations, Appl. Numer. Math. 18 (1995) 241-251.